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We consider a birth–death process with birth rates  and death rates +(1), where  is the current state of the process. A positive competition rate  is assumed to be small. In the supercritical case where , this process can be viewed as a demographic model for a population with high carrying capacity around (). The article reports in a self-contained manner on the asymptotic properties of the time to extinction for this logistic branching process as  0. All three reproduction regimes , , and  =  are studied.

Extinction times for a birth–death process with weak competition